Effect of quantum modes in biological electron transfer reactions: A useful approximation for the harmonic model with frequency change and Duchinsky rotation

Although general theory of quantum effects in nonadiabatic electron transfe r (ET) reactions based on spin-boson Hamiltonian is well known, its applica tion to problems of biological interest is hampered by the amount of comput ational work needed to map the details of the real system onto the paramete rs of the model. In this paper we propose a new formulation of theory of qu antum effects which remedies many defects of the usual approach. In the har monic approximation an exact expression for the rate of electron transfer h as long been known that includes effects of frequency change and Duchinsky rotation (mixing) of vibrational modes of donor and acceptor complexes. Thi s expression, however, is not suitable for practical applications due to it s complexity. We have developed an exceptionally accurate approximation tha t is capable of capturing all details of real redox systems typical for bio logical problems, yet simple enough to be practical. The approximation is b ased on the well-known Jortner expression for the quantum rate. We describe a method for calculation of the parameters of the Jortner model, average q uantum frequency and average excitation number, which are usually treated a s adjustable parameters, and in our case are calculated by ab initio quantu m chemistry methods. The model is tested against the exact result. We also have tested another useful approximation, which is as good as the first one , however, in a limited region around maximum of ET rate. In this approxima tion the rate constant has the same form as the semiclassical Marcus expres sion, except that instead of one reorganization energy lambda, it contains two lambda's. We show how these parameters can be calculated for realistic systems. Examples of such calculations are presented for a novel electron t ransfer between tryptophan and tyrosine, which was discovered recently in p hotolyase, a DNA repair enzyme, and some other biological systems. (C) 2000 American Institute of Physics. [S0021-9606(00)70413-2].